Theory of Three-Magnon Ferromagnetic Relaxation Frequency for Low Temperatures and Small Wave Vectors

The three-magnon confluence relaxation frequency $\frac{1}{\ensuremath{\tau}}$ is calculated without making assumptions of the previous calculation of Sparks, Loudon, and Kittel. The results are such that the discrepancies between the experiments of Comstock, LeCraw, Nilsen, Remeika, Spencer, and Walker and the previous theory are removed. In particular, the exponentially small (rather than linear) dependence of $\frac{1}{\ensuremath{\tau}}$ on ${k}_{1}$ and $T$ is explained by the new theory. A calculation of the bending down of $\frac{1}{\ensuremath{\tau}}$ below linearity in ${k}_{1}$ at large values of ${k}_{1}$ is also given.All pertinent experimental results reported to date agree qualitatively with the new theoretical results; several experiments agree extremely well quantitatively. For example, LeCraw and Spencer's $\frac{1}{\ensuremath{\tau}}'\mathrm{s}$ are within 7% of the new theoretical values for all ${k}_{1}$ between 0.4\ifmmode\times\else\texttimes\fi{}${10}^{5}$ and 2.1\ifmmode\times\else\texttimes\fi{}${10}^{5}$ ${\mathrm{cm}}^{\ensuremath{-}1}$. In other experiments, the observed values of $\frac{1}{\ensuremath{\tau}}$ are considerably larger than the theoretical values (an order of magnitude in the worst case); it appears that some other process is operative in these experiments. Measurements on ultrahigh-purity samples would be helpful in identifying this process.